Tag
Classical Mechanics
Classical mechanics describes the motion of bodies under Newton's laws, from a single point mass to a rigid body rotating in three dimensions, together with its variational reformulation through the Lagrangian and Hamiltonian formalisms. Central objects include momentum, angular momentum, the inertia tensor, and the action functional, whose stationary points give the equations of motion via the Euler-Lagrange equations. My interest is in the two computational languages available for the same physics, matrix and vector calculus alongside geometric algebra, which replaces Euler angles and the cross product with rotors and bivectors.
Blog
July 29, 2026
A High School Student's Introduction to Physics
Physics built from arithmetic, assuming nothing beyond addition and subtraction. The number systems and the equals sign, then units, then the affine space of positions, then the geometric product forced by the demand that a vector square to its own length. The calculus is constructed on the way, with the limit stated in full and the derivative defined by Caratheodory's slope function. In the geometric algebra of the plane: the kinematic formulas derived as a corollary of integrating a constant, centripetal acceleration by differentiating a rotor twice, the harmonic oscillator's cosine proved rather than announced, angular momentum as a conserved bivector with Kepler's equal areas as its consequence, and work and energy as the fundamental theorem along a path.
July 3, 2026
Classical Mechanics from Zero, in Two Languages
Classical mechanics constructed from nothing but an inertial frame, in matrix and linear algebra and in geometric algebra side by side: rotations and rigid-body dynamics without Euler angles, one vector derivative replacing grad, div, and curl, and the Lagrangian and Hamiltonian formalisms in both languages.